This paper is concerned with a parallel solution of the Sylvester matrix equation AX+XB=C by means of the iterative method of successive approximations. In this work convergence conditions for the method are given. If the matrices A and B have a block partitioned form, different choices of the splittings of A and B are presented. In this case at each iteration of the method, one has to solve a set of independent Sylvester equations, which can be solved in parallel by means of a direct method. By using the multisplitting principle it has been also introduced an explicit parallelism in the method. The implementation of the iterative method on a distributed memory system such as Cray T3D has been described and the results of some computational experiments related to the solution of the Riccati equation, have been presented.
Solution of the Sylvester equation on a parallel computer / Galligani, Emanuele. - STAMPA. - 11, Series: Advances in Parallel Computing, Ed. G.R. JOUBERT:(1996), pp. 189-195. (Intervento presentato al convegno International Conference ParCo95 tenutosi a Gand nel 19-22 settembre, 1995).
Solution of the Sylvester equation on a parallel computer
GALLIGANI, Emanuele
1996
Abstract
This paper is concerned with a parallel solution of the Sylvester matrix equation AX+XB=C by means of the iterative method of successive approximations. In this work convergence conditions for the method are given. If the matrices A and B have a block partitioned form, different choices of the splittings of A and B are presented. In this case at each iteration of the method, one has to solve a set of independent Sylvester equations, which can be solved in parallel by means of a direct method. By using the multisplitting principle it has been also introduced an explicit parallelism in the method. The implementation of the iterative method on a distributed memory system such as Cray T3D has been described and the results of some computational experiments related to the solution of the Riccati equation, have been presented.
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